xercise 11-1 Assume the weight of a bag of microwave popcorn from a certain brand varies
according to a normal distribution with mean = 2.69 oz and standard deviation = 0.05 oz.
Suppose Benji was skeptical about the manufacturers claim that the mean is 2.69 oz, so he took a
random sample of 12 bags of the popcorn and weighed them. Their sample mean weight was
2.65 ounces. (a) Apply the Central Limit Theorem for a sample mean to draw a sketch of the
sampling distribution of the sample mean weights of bags of this microwave popcorn if samples
of size n = 12 were taken over and over. Note its center (measured by the mean), spread
(measured by standard deviation), and shape. (b) Is it plausible to get a sample mean weight this
small (2.65 ounces) even if the manufacturers claim is true? Explain, referring to the graph you
sketched in (a). (c) Should Benji continue to be skeptical that the manufacturers claim is true?
Explain, referring to the graph you sketched in (a). (d) What values for the sample mean weight
would provide fairly strong evidence against the manufacturers claim? Explain, again referring
to the sampling distribution sketched in